Expert: Paul Klarreich - 5/24/2008

Question
I am doing a math project and I have to set this equation equal to one another and solve for t using logarithms.
500(1.02)^(4t)=1000e^(.05x)

the question is how many years will it take account G= 500(1.02)^(4t)to equal the balance of account h= 1000e^(.05x)? what will the account balances be at this time?

Answer
Questioner:   Alexis
Category:  Advanced Math
Private:  No
 
Subject:  Algebra
Question:  I am doing a math project and I have to set this equation equal to one another and solve for t using logarithms.
500(1.02)^(4t)=1000e^(.05x)

the question is how many years will it take account G= 500(1.02)^(4t)to equal the balance of account h= 1000e^(.05x)? what will the account balances be at this time?
...................................................
Hi, Alexis:

Did you mean to write:

500(1.02)^(4t)=1000e^(.05t) << you wrote x here.

In that case, you use natural logarithms to write:
(after dividing out the 500.)

(1.02)^(4t) = 2e^(.05t)

4t ln (1.02) = ln 2 + 0.05t

4t - 0.05t = ln 2 - ln(1.02)

3.95t = ln 2 - ln(1.02)
   ln 2 - ln(1.02)
t = ---------------
       3.95

Now just use your calculator.  You should be able to handle the rest.